Identifier
-
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
St000366: Permutations ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>0
[1,0,1,0]=>[1,2]=>0
[1,1,0,0]=>[2,1]=>0
[1,0,1,0,1,0]=>[1,2,3]=>0
[1,0,1,1,0,0]=>[1,3,2]=>0
[1,1,0,0,1,0]=>[2,1,3]=>0
[1,1,0,1,0,0]=>[2,3,1]=>0
[1,1,1,0,0,0]=>[3,2,1]=>1
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>0
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>0
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>0
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>0
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>1
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>0
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>0
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>0
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>0
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>1
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>1
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>0
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>1
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>2
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>0
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>0
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>0
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>0
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>1
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>0
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>0
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>0
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>0
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>1
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>1
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>0
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>1
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>2
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>0
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>0
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>0
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>0
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>1
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>0
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>0
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>0
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>0
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>1
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>1
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>0
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>1
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>2
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>1
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>1
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>0
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>0
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>1
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>1
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>0
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>1
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>2
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>2
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>1
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>1
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>2
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>3
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>0
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>0
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>0
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>0
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>0
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>0
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>0
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>1
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>0
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>2
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>0
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>0
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>0
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>0
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>0
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>0
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>0
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>0
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>1
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>0
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>2
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>0
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>0
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>0
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>1
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>2
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>3
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>0
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>0
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>0
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>0
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>0
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>0
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>0
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>0
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>1
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>0
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>1
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>0
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>0
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>0
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>0
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>1
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>0
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>0
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>0
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>0
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>0
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>0
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>0
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>0
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>2
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>2
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>1
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>2
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>0
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>0
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>0
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>0
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>0
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>2
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>0
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>0
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>1
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>0
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>2
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>2
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>2
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>0
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>2
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>3
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>2
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>2
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>3
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>4
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>4
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>0
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>0
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>0
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>0
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>0
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>0
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>4
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>0
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>0
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>4
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>4
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>4
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>4
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>6
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,6,5,4,3,2,1,9]=>5
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,7,6,5,4,3,2]=>5
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>7
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,7,6,5,4,3,2,1,10]=>6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,6,8,5,4,3,2,1,9]=>4
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,8,7,5,4,3,2,1,9]=>5
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,7,9,6,5,4,3,2]=>4
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,7,9,8,6,5,4,3,2]=>5
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9,10,8,7,6,5,4,3,2]=>6
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>5
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>6
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>6
[]=>[]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>0
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,1]=>0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>0
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>0
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,7,6,5,4,3,10,9]=>4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,6,5,10,9,8,7]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,8,7,6,5,10,9]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9,10]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>5
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>8
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>8
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Description
The number of double descents of a permutation.
A double descent of a permutation $\pi$ is a position $i$ such that $\pi(i) > \pi(i+1) > \pi(i+2)$.
A double descent of a permutation $\pi$ is a position $i$ such that $\pi(i) > \pi(i+1) > \pi(i+2)$.
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to 312-avoiding permutation
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